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/usr/bin/how-many-binary is in what-utils 1.5-0ubuntu1.

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#!/bin/sh
#
#    how-many-binary - how many binary packages in Ubuntu
#
#    Copyright (C) 2016 Dustin Kirkland <kirkland@ubuntu.com>
#
#    Authors:
#        Dustin Kirkland <kirkland@ubuntu.com>
#
#    This program is free software: you can redistribute it and/or modify
#    it under the terms of the GNU General Public License as published by
#    the Free Software Foundation, either version 3 of the License.
#
#    This program is distributed in the hope that it will be useful,
#    but WITHOUT ANY WARRANTY; without even the implied warranty of
#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#    GNU General Public License for more details.
#
#    You should have received a copy of the GNU General Public License
#    along with this program.  If not, see <http://www.gnu.org/licenses/>.

arch="amd64"
. /etc/lsb-release 2>/dev/null || true
release=$DISTRIB_CODENAME
VERBOSE=0
for i in $@; do
	case "$i" in
		-a|--arch|--architecture)
			arch="$2"
			shift 2
		;;
		-r|--release)
			release="$2"
			shift 2
		;;
		-v|--verbose)
			VERBOSE=1
			shift
		;;
	esac
done

dir=$(mktemp -d)
trap "rm -rf ${dir}" HUP INT QUIT ILL TRAP KILL BUS TERM
cd "$dir"

case "$arch" in
	amd64|x86_64|*86)
		archive="archive.ubuntu.com/ubuntu"
	;;
	*)
		archive="ports.ubuntu.com/ubuntu-ports"
	;;
esac

for i in main universe restricted multiverse; do
	u="http://$archive/dists/$release/$i/binary-$arch/Packages.gz"
	wget -q -O $i.gz "$u" >/dev/null 2>&1
done
if [ "$VERBOSE" = "1" ]; then
	zgrep "^Filename:.*\.deb$" * | sort -u
fi
zgrep "^Package:" * | sort -u | wc -l